ENG202 Engineering Mathematics II (3+0+0 3 Units)

Partial Differentiation: Functions of several variables, continuity and partial derivatives.

Total differentials, approximate calculations using differentials.

Chain rule. Implicit differentiation. Series representation of functions (Maclaurin & Taylor’s), Taylor’s Theorem. Extremum problems, (analytic method) without and with constraints, Lagrange multipliers, global extremum.

Ordinary Differential Equations: Definition, degree, order, linear, nonlinear, solution. First order equations, separable variables, equations reducible to separable form, exact equations, integrating factors, homogenous differential equations.

Modeling of engineering systems leading to first order differential equations electric circuit, mixing/dilution, radioactive decay, bacterial culture.

2nd order differential equations with constant coefficients, homogeneous, nonhomogeneous, complementary functions, particular integrals, Doperator method. General linear secondorder differential equations (without using matrices).Power series solution, Legendre’s differential equation.

Modeling of engineering systems leading to 2nd order differential equations electric circuit, Mechatronics oscillationsfree and forced, resonance.

Matrices and Determinants: Solution of system of linear equations by determinants. Linear dependence and independence, rank of a matrix. General system of linear equations, existence and properties of solution, Gaussian elimination. Matrix inverse by elementary matrices, adjoint, and partitioning methods. Characteristic polynomial, characteristic equation, eigenvalues and eigenvectors.